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Electrons diffract through crystal lattices or slits, producing interference patterns identical to those of light, with spacing inversely proportional to electron momentum. Double-slit experiments with electrons demonstrate that individual electrons do not take definite paths but exist in superposition. This confirms that matter possesses genuine wave properties that affect its propagation.
From de Broglie's hypothesis — your prerequisite — you know that any particle with momentum p has an associated wavelength λ = h/p. From the Davisson-Germer experiment, you know that electrons scattered from a nickel crystal produced an interference pattern whose angular positions matched Bragg diffraction calculated using this de Broglie wavelength. That experiment confirmed that the hypothesis is not merely a mathematical curiosity but a physical reality: electrons genuinely behave as waves when they encounter structures whose spacing is comparable to their wavelength.
What makes electron diffraction conceptually deeper than confirming a formula is what it says about the nature of the electron's path. In the classic double-slit experiment performed with electrons, a beam of electrons is directed at a barrier with two narrow slits. If you block one slit, you get a single broad diffraction pattern on the detector. If you open both slits, you do not get the sum of two single-slit patterns — you get an interference pattern with alternating bright and dark fringes, just as with light. This already suggests wave behavior. But the truly startling version is when electrons are sent one at a time, so slowly that only one electron is in the apparatus at any moment. Each electron lands at a single point on the detector, as a particle would. But as millions of electrons accumulate, they build up the same interference pattern. No individual electron "knew" about the other electrons; yet the statistical distribution of landing positions displays wave interference.
The inescapable conclusion is that the interference is a property of each individual electron, not a collective effect. Each electron does not take a definite path through one slit or the other — it exists in a superposition of going through both slits, and the two amplitudes interfere. If you place a detector at the slits to determine which path the electron took, the interference pattern disappears. The act of measurement collapses the superposition and forces a definite path, eliminating the interference. This is not a technical limitation but a fundamental feature of quantum mechanics.
The connection between wavelength and momentum is quantitative and testable. Electrons accelerated through a potential difference V acquire kinetic energy eV = p²/2m, giving momentum p = √(2meV) and wavelength λ = h/√(2meV). At 100 V, λ ≈ 0.12 nm — comparable to atomic spacings, which is why crystal diffraction works so well. At higher energies (shorter wavelengths), electron diffraction becomes a precision tool for determining crystal structure and atomic spacing in materials science, just as X-ray crystallography does — but electrons interact far more strongly with matter, making them ideal for surface studies. The wave nature of matter is not an abstraction; it is the operating principle behind electron microscopes, electron crystallography, and quantum interference devices.